Ch.19 - Free Energy & Thermodynamics

Tro - Chemistry: A Molecular Approach 6th Edition

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Tro 6th Edition

Ch.19 - Free Energy & Thermodynamics

Problem 51

Chapter 19, Problem 51

How does the molar entropy of a substance change with increasing temperature?

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Understand that entropy is a measure of the disorder or randomness in a system. As temperature increases, the kinetic energy of the molecules also increases.

Recognize that with increased kinetic energy, molecules move more vigorously, leading to greater disorder or randomness in the system.

Recall that the molar entropy of a substance is directly related to the number of accessible microstates. As temperature increases, more microstates become accessible to the molecules.

Consider that the increase in accessible microstates with temperature results in an increase in the molar entropy of the substance.

Conclude that generally, the molar entropy of a substance increases with increasing temperature due to the increased molecular motion and the greater number of accessible microstates.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molar Entropy

Molar entropy is a measure of the amount of disorder or randomness in a system per mole of substance. It reflects the number of accessible microstates for a given macrostate, with higher entropy indicating greater disorder. This concept is crucial for understanding thermodynamic processes and predicting how substances behave under varying conditions.

Temperature and Entropy Relationship

As temperature increases, the kinetic energy of particles in a substance also increases, leading to greater molecular motion. This heightened motion allows for more possible arrangements of particles, thereby increasing the molar entropy. The relationship between temperature and entropy is fundamental in thermodynamics, particularly in the context of the second law of thermodynamics.

Second Law of Thermodynamics

The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. It implies that natural processes tend to move towards a state of maximum disorder or entropy. Understanding this law helps explain why the molar entropy of substances generally increases with temperature, as systems evolve towards higher entropy states.

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Related Practice

Textbook Question

Predict the conditions (high temperature, low temperature, all temperatures, or no temperatures) under which each reaction is spontaneous. a. H₂O(g) → H₂O(l) b. CO₂(s) → CO₂(g) c. H₂(g) → 2 H(g) d. 2 NO₂(g) → 2 NO(g) + O₂(g) (endothermic)

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Textbook Question

For each pair of substances, choose the one that you expect to have the higher standard molar entropy (S°) at 25 °C. Explain your choices. a. CO(g); CO₂(g) b. CH₃OH(l); CH₃OH(g) c. Ar(g); CO₂(g) d. CH₄(g); SiH₄(g) e. NO₂(g); CH₃CH₂CH₃(g) f. NaBr(s); NaBr(aq)

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Textbook Question

Calculate the change in Gibbs free energy for each of the sets of ΔH°_rxn, ΔS°_rxn, and T given in Problem 44. Predict whether or not each reaction is spontaneous at the temperature indicated. (Assume that all reactants and products are in their standard states.)

Textbook Question

Rank each set of substances in order of increasing standard molar entropy (S°). Explain your reasoning. a. I₂(g); F₂(g); Br₂(g); Cl₂(g) b. H₂O(g); H₂O₂(g); H₂S(g) c. C(s, graphite); C(s, diamond); C(s, amorphous)

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Textbook Question

Rank each set of substances in order of increasing standard molar entropy (S°). Explain your reasoning. a. NH₃(g); Ne(g); SO₂(g); CH₃CH₂OH(g); He(g) c. CH₄(g); CF₄(g); CCl₄(g)

Calculate the free energy change for this reaction at 25 °C. Is the reaction spontaneous? (Assume that all reactants and products are in their standard states.) 2 Ca(s) + O₂( g) → 2 CaO(s) ΔH°_rxn = -1269.8 kJ; ΔS°_rxn = -364.6 J/K

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